partial equivalence relation

(PER) A relation R on a set S where R is symmetric (x R y => y R x) and
transitive (x R y R z => x R z) and where there may exist elements in S for
which the relation is not defined. A PER is an equivalence relation on the
subset for which it is defined, i.e. it is also reflexive (x R x).

Since n is known we can specialise pow in its second argument and unfold
the recursive calls:

pow5 x = x * x4 where x4 = x2 * x2
x2 = x * x
f x = pow5 x

pow5 is known as the residual. We could now also unfold pow5 giving:

f x = x * x4 where x4 = x2 * x2
x2 = x * x

It is important that the partial evaluation algorithm should terminate.
This is not guaranteed in the presence of recursive
function definitions. For example, if partial
evaluation were applied to the right hand side of
the second clause for pow above, it would never
terminate because the value of n is not known.

Partial evaluation might change the termination properties of the program if,
for example, the expression (x * 0) was reduced to 0 it would terminate even if
x (and thus x * 0) did not.

It may be necessary to reorder an expression to partially evaluate it, e.g.

f x y = (x + y) + 1
g z = f 3 z

If we rewrite f:

f x y = (x + 1) + y

then the expression x+1 becomes a constant for the function g and we can
say

g z = f 3 z = (3 + 1) + z = 4 + z

Partial evaluation of built-in functions applied to constant arguments is
known as constant folding.

partially ordered set

partial ordering

A relation R is a partial ordering if it is a pre-order (i.e. it is reflexive (x
R x) and transitive (x R y R z => x R z)) and it is also antisymmetric (x R y R
x => x = y). The ordering is partial, rather than total, because there may exist
elements x and y for which neither x R y nor y R x.

In domain theory, if D is a set of values including the undefined value (bottom)
then we can define a partial ordering relation <= on D by

x <= y if x = bottom or x = y.

The constructed set D x D contains the very undefined element, (bottom,
bottom) and the not so undefined elements, (x,
bottom) and (bottom, x). The partial ordering on D x
D is then

(x1,y1) <= (x2,y2) if x1 <= x2 and y1 <= y2.

The partial ordering on D -> D is defined by

f <= g if f(x) <= g(x) for all x in D.

(No f x is more defined than g x.)

A lattice is a partial ordering where all finite subsets have a least upper
bound and a greatest lower bound.

Partial Response Maximum Likelihood

<storage> (PRML) A method for converting the weak analog signal from the
head of a magnetic disk drive into a digital signal. PRML attempts to correctly
interpret even small changes in the analog signal, whereas peak detection relies
on fixed thresholds. Because PRML can correctly decode a weaker signal it allows
higher density recording.

For example, PRML would read the magnetic flux density pattern 70, 60, 55, 60,
70 as binary "101", and the same for 45, 40, 30, 40, 45. A peak detector would
decode everything above, say, 50 as high, and below 50 as low, so the first
pattern would read "111" and the second as "000".

partitioned data set

<file format> (PDS) A data set on an IBM mainframe that contains members,
each of which acts like a separate data set. Partitioned data sets are more
space-efficient than individual data sets, because they can put more than one
data set on a track. They are also used to hold libraries, with one function per
member. The syntax for a member is NAME.OF.PDS(MEMBER) although some systems
(such as Phoenix) could use NAME.OF.PDS:MEMBER

Original PDSes were of fixed size, and needed frequent compression to recover
space after deleting or changing members. Newer PDS/E Extended PDSes do not have
this problem.

PARTS

@-party

<event> /at'par-tee/ (Or "@-sign party" /at'si:n par'tee/, from the @
sign in an electronic mail address) A semi-closed party thrown for hackers at a
science-fiction convention (especially the annual Worldcon); one must have an
electronic mail address to get in, or at least be in company with someone who
does. One of the most reliable opportunities for hackers to meet face-to-face
with people who might otherwise be represented by mere phosphor dots on their
screens.